Trying to put this together ...
Prof. Kano’s penname, until he was 60, was “Kônan (甲南).” During his 60's, he wrote under the name “Shinkosaï (進乎斎)” changing it again to “Ki-Issaï (帰一斎)” in his 70’s.
“Shinkosaï” was inspired by a phrase of Zhuangzi (荘子), an ancient Chinese philosopher. Echoing an ancient story regarding a cook who valued “the way” more than skills, Prof. Kano intended to include the value-based meaning in his penname “Shinkosaï” stressing the importance of pursuing one's path as a human being rather than acquiring skills.
If I translate “Shinkosaï (進乎斎)” I get to "advance in fasting". 斎 is a japanese variant of 齋 "zhai" (fasting). "zhai" is as a compound with 心 (xin, heart, heartmind) "the fasting of the mind" (in TCM "xin" the heart, is not only the location for emotions but also for thoughts and will etc.).
"Fasting of the mind" (xin zhai) is one of the core ideas of the Zhuangzi but also 德 "De" http://en.wikipedia.org/wiki/De_%28Chinese%29
To put the stories together:
A) The Cook, skills and Dao (way, method)
His cook was cutting up an ox for the ruler Wen Hui. Whenever he applied his hand, leaned forward with his shoulder, planted his foot, and employed the pressure of his knee, in the audible ripping off of the skin, and slicing operation of the knife, the sounds were all in regular cadence. Movements and sounds proceeded as in the dance of 'the Mulberry Forest' and the blended notes of the King Shou.' The ruler said, 'Ah! Admirable! That your art should have become so perfect!' (Having finished his operation), the cook laid down his knife, and replied to the remark, 'What your servant loves is the method of the Dao, something in advance of any art. When I first began to cut up an ox, I saw nothing but the (entire) carcase. After three years I ceased to see it as a whole. Now I deal with it in a spirit-like manner, and do not look at it with my eyes. The use of my senses is discarded, and my spirit acts as it wills. Observing the natural lines, (my knife) slips through the great crevices and slides through the great cavities, taking advantage of the facilities thus presented. My art avoids the membranous ligatures, and much more the great bones. A good cook changes his knife every year; (it may have been injured) in cutting - an ordinary cook changes his every month - (it may have been) broken. Now my knife has been in use for nineteen years; it has cut up several thousand oxen, and yet its edge is as sharp as if it had newly come from the whetstone. There are the interstices of the joints, and the edge of the knife has no (appreciable) thickness; when that which is so thin enters where the interstice is, how easily it moves along! The blade has more than room enough. Nevertheless, whenever I come to a complicated joint, and see that there will be some difficulty, I proceed anxiously and with caution, not allowing my eyes to wander from the place, and moving my hand slowly. Then by a very slight movement of the knife, the part is quickly separated, and drops like (a clod of) earth to the ground. Then standing up with the knife in my hand, I look all round, and in a leisurely manner, with an air of satisfaction, wipe it clean, and put it in its sheath.' The ruler Wen Hui said, 'Excellent! I have heard the words of my cook, and learned from them the nourishment of (our) life.'
B) Fasting of the Mind
Yan Hui said, 'I can go no farther; I venture to ask the method from you.' Zhongni replied, 'It is fasting, (as) I will tell you. (But) when you have the method, will you find it easy to practise it? He who thinks it easy will be disapproved of by the bright Heaven.' Hui said, 'My family is poor. For months together we have no spirituous drink, nor do we taste the proscribed food or any strong-smelling vegetables;-- can this be regarded as fasting?' The reply was, 'It is the fasting appropriate to sacrificing, but it is not the fasting of the mind.' 'I venture to ask what that fasting of the mind is,' said Hui, and Zhongni answered,
'Maintain a perfect unity in every movement of your will, You will not wait for the hearing of your ears about it, but for the hearing of your mind. You will not wait even for the hearing of your mind, but for the hearing of the spirit. Let the hearing (of the ears) rest with the ears. Let the mind rest in the verification (of the rightness of what is in the will). But the spirit is free from all pre-occupation and so waits for (the appearance of) things. Where the (proper) course is, there is freedom from all pre-occupation; such freedom is the fasting of the mind.'
If Kano Shihan refers (it is no direct quote...) with his second pen name “Shinkosaï (進乎斎)” "advance in fasting" to the Zhuangzi, it should be the second story as a core (inner practice) and the first story as an output (outer practice).
But maybe he only wanted to eat less ...